A phase plane analysis of neuron-astrocyte interactions

From quiescence to self-sustained activity: How astrocytes reshape neural dynamics

Astrocytes are currently gaining attention from the neuroscience community due to their contribution to a multitude of functions, which includes but are not limited to their ability to change the neuron's spiking frequency, their capacity to alter neuron's firing activity, and their involvement in memory formation and synaptic plasticity regulation. To date, many computational models describing the dynamics of astrocytes, together with their complex interaction with neurons, were proposed, however, these could still be improved since the exploration of their functions and mechanisms was way later than neurons. Hence, in this paper, investigation of the steady state behavior of the neuron-astrocyte interaction through a presentation of phase plane analysis and one parameter bifurcation were primarily performed. Adaptive Exponential Integrate-and-Fire model was utilized to describe the firing dynamics of the neuron while the model from the work of Postnov and collaborators was used to describe the calcium dynamics of the astrocyte. The findings demonstrate that astrocytic modulation can significantly shape neuronal activity, including initiating spikes, inducing self-sustained oscillations, and exerting both inhibitory and excitatory effects depending on synaptic strength. These highlight the crucial role that the contribution of astrocytes to the synapse plays in regulating neuronal activity and producing a range of neuronal firing behaviors within the neuron-astrocyte ensemble. They may impact neuronal synchronization, an attribute of several neurological illnesses, including epilepsy, and, on the other hand, may enhance brain information processing.

Dynamical modeling and analysis of epileptic discharges transition caused by glutamate release with metabolism processes regulation from astrocyte

Glutamate (Glu) is a crucial excitatory neurotransmitter in the central nervous system that transmits brain information by activating excitatory receptors on neuronal membranes. Physiological studies have demonstrated that abnormal Glu metabolism in astrocytes is closely related to the pathogenesis of epilepsy. The astrocyte metabolism processes mainly involve the Glu uptake through astrocyte EAAT2, the Glu-glutamine (Gln) conversion, and the Glu release. However, the relationship between these Glu metabolism processes and epileptic discharges remains unclear. In this paper, we propose a novel neuron-astrocyte model by integrating the dynamical modeling of astrocyte Glu metabolism processes, which include Glu metabolism in astrocytes consisting of the Glu uptake, Glu-Gln conversion, Glu diffusion, and the resulting Glu release as well as Glu-mediated bidirectional communication between neuron and astrocyte. Furthermore, the influences of astrocyte multiple Glu metabolism processes on the Glu release and dynamics transition of neuronal epileptic discharges are verified through numerical experiments and dynamical analyses from various nonlinear dynamics perspectives, such as time series, phase plane trajectories, interspike intervals, and bifurcation diagrams. Our results suggest that the downregulation expression of EAAT2 uptake, the slowdown of the Glu-Gln conversion rate, and excessively elevated Glu equilibrium concentration in astrocytes can cause an increase in Glu released from astrocytes, which results in the aggravation of epileptic seizures. Meanwhile, neuronal epileptic discharge states transition from bursting to mixed-mode spiking and tonic firing induced by the combination of these abnormal metabolism processes. This study provides a theoretical foundation and dynamical analysis methodology for further exploring the dynamics evolution and physiopathological mechanisms of epilepsy.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

Analysis of Network Models with Neuron-Astrocyte Interactions

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures, which convey complex dynamical characteristics including chaos and randomness. Until now, the underlying mechanism has not been fully elucidated, especially the bistable property beneath the epileptic random induction phenomena in certain conditions. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messenger, inositol triphosphate (IP3) that is modulated by G-protein-coupled receptor activation. Based on this model, we have statistically analyzed the transitions of epileptic seizures by performing repeatable simulation trials. Our simulation results show that the increase in the IP3 noise intensity induces depolarization-block epileptic seizures together with an increase in neuronal firing frequency, consistent with corresponding experiments. Meanwhile, the bistable states of the seizure dynamics were present under certain noise intensities, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness in certain conditions.

Exosomes and exosomal microRNA in non-targeted radiation bystander and abscopal effects in the central nervous system

Localized cranial radiotherapy is a dominant treatment for brain cancers. After being subjected to radiation, the central nervous system (CNS) exhibits targeted effects as well as non-targeted radiation bystander effects (RIBE) and abscopal effects (RIAE). Radiation-induced targeted effects in the CNS include autophagy and various changes in tumor cells due to radiation sensitivity, which can be regulated by microRNAs. Non-targeted radiation effects are mainly induced by gap junctional communication between cells, exosomes containing microRNAs can be transduced by intracellular endocytosis to regulate RIBE and RIAE. In this review, we discuss the involvement of microRNAs in radiation-induced targeted effects, as well as exosomes and/or exosomal microRNAs in non-targeted radiation effects in the CNS. As a target pathway, we also discuss the Akt pathway which is regulated by microRNAs, exosomes, and/or exosomal microRNAs in radiation-induced targeted effects and RIBE in CNS tumor cells. As the CNS-derived exosomes can cross the blood-brain-barrier (BBB) into the bloodstream and be isolated from peripheral blood, exosomes and exosomal microRNAs can emerge as promising minimally invasive biomarkers and therapeutic targets for radiation-induced targeted and non-targeted effects in the CNS.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

The brain as a "hyper-network": the key role of neural networks as main producers of the integrated brain actions especially via the "broadcasted" neuroconnectomics

Investigations of brain complex integrative actions should consider beside neural networks, glial, extracellular molecular, and fluid channels networks. The present paper proposes that all these networks are assembled into the brain hyper-network that has as fundamental components, the tetra-partite synapses, formed by neural, glial, and extracellular molecular networks. Furthermore, peri-synaptic astrocytic processes by modulating the perviousness of extracellular fluid channels control the signals impinging on the tetra-partite synapses. It has also been surmised that global signalling via astrocytes networks and highly pervasive signals, such as electromagnetic fields (EMFs), allow the appropriate integration of the various networks especially at crucial nodes level, the tetra-partite synapses. As a matter of fact, it has been shown that astrocytes can form gap-junction-coupled syncytia allowing intercellular communication characterised by a rapid and possibly long-distance transfer of signals. As far as the EMFs are concerned, the concept of broadcasted neuroconnectomics (BNC) has been introduced to describe highly pervasive signals involved in resetting the information handling of brain networks at various miniaturisation levels. In other words, BNC creates, thanks to the EMFs, generated especially by neurons, different assemblages among the various networks forming the brain hyper-network. Thus, it is surmised that neuronal networks are the "core components" of the brain hyper-network that has as special "nodes" the multi-facet tetra-partite synapses. Furthermore, it is suggested that investigations on the functional plasticity of multi-partite synapses in response to BNC can be the background for a new understanding and perhaps a new modelling of brain morpho-functional organisation and integrative actions.

Digital Implementation of the Two-Compartmental Pinsky-Rinzel Pyramidal Neuron Model

It is believed that brain-like computing system can be achieved by the fusion of electronics and neuroscience. In this way, the optimized digital hardware implementation of neurons, primary units of nervous system, play a vital role in neuromorphic applications. Moreover, one of the main features of pyramidal neurons in cortical areas is bursting activities that has a critical role in synaptic plasticity. The Pinsky-Rinzel model is a nonlinear two-compartmental model for CA3 pyramidal cell that is widely used in neuroscience. In this paper, a modified Pinsky-Rinzel pyramidal model is proposed by replacing its complex nonlinear equations with piecewise linear approximation. Next, a digital circuit is designed for the simplified model to be able to implement on a low-cost digital hardware, such as field-programmable gate array (FPGA). Both original and proposed models are simulated in MATLAB and next digital circuit simulated in Vivado is compared to show that obtained results are in good agreement. Finally, the results of physical implementation on FPGA are also illustrated. The presented circuit advances preceding designs with regards to the ability to replicate essential characteristics of different firing responses including bursting and spiking in the compartmental model. This new circuit has various applications in neuromorphic engineering, such as developing new neuroinspired chips.

A new bio-inspired stimulator to suppress hyper-synchronized neural firing in a cortical network

Hyper-synchronous neural oscillations are the character of several neurological diseases such as epilepsy. On the other hand, glial cells and particularly astrocytes can influence neural synchronization. Therefore, based on the recent researches, a new bio-inspired stimulator is proposed which basically is a dynamical model of the astrocyte biophysical model. The performance of the new stimulator is investigated on a large-scale, cortical network. Both excitatory and inhibitory synapses are also considered in the simulated spiking neural network. The simulation results show that the new stimulator has a good performance and is able to reduce recurrent abnormal excitability which in turn avoids the hyper-synchronous neural firing in the spiking neural network. In this way, the proposed stimulator has a demand controlled characteristic and is a good candidate for deep brain stimulation (DBS) technique to successfully suppress the neural hyper-synchronization.

A digital neurmorphic circuit for a simplified model of astrocyte dynamics

Recent neurophysiologic findings have shown that astrocytes (the most abundant type of glial cells) are active partners in neural information processing and regulate the synaptic transmission dynamically. Motivated by these findings, in the present research, a digital neuromorphic circuit to implement the astrocyte dynamics is developed. To model the dynamics of the intracellular Ca(2+) waves produced by astrocytes, we utilize a simplified model which considers the main physiological pathways of neuron-astrocyte interactions. Next, a digital circuit for the astrocyte dynamic is proposed which is simulated using ModelSim and finally, it is implemented in hardware on the ZedBoard. The results of hardware synthesis, FPGA implementations are in agreement with MATLAB and ModelSim simulations and confirm that the proposed digital astrocyte is suitable for applications in reconfigurable neuromorphic devices which implement biologically brain circuits.

Information handling by the brain: proposal of a new "paradigm" involving the roamer type of volume transmission and the tunneling nanotube type of wiring transmission

The current view on the organization of the central nervous system (CNS) is basically anchored to the paradigm describing the brain as formed by networks of neurons interconnected by synapses. Synaptic contacts are a fundamental characteristic for describing CNS operations, but increasing evidence accumulated in the last 30 years pointed to a refinement of this view. A possible overcoming of the classical "neuroscience paradigm" will be here outlined, based on the following hypotheses: (1) the basic morpho-functional unit in the brain is a compartment of tissue (functional module) where different resident cells (not only neurons) work as an integrated unit; (2) in these complex networks, a spectrum of intercellular communication processes is exploited, that can be classified according to a dichotomous criterion: wiring transmission (occurring through physically delimited channels) and volume transmission (exploiting diffusion in the extracellular space); (3) the connections between cells can themselves be described as a network, leading to an information processing occurring at different levels from cell network down to molecular level; (4) recent evidence of the existence of specialized structures (microvesicles and tunneling nanotubes) for intercellular exchange of materials, could allow a further type of polymorphism of the CNS networks based on at least transient changes in cell phenotype. When compared to the classical paradigm, the proposed scheme of cellular organization could allow a strong increase of the degrees of freedom available to the whole system and then of its plasticity. Furthermore, long range coordination and correlation can be more easily accommodated within this framework.

Astrocyte-neuron interactions: from experimental research-based models to translational medicine

In this chapter, we review the principal astrocyte functions and the interactions between neurons and astrocytes. We then address how the experimentally observed functions have been verified in computational models and review recent experimental literature on astrocyte-neuron interactions. Benefits of computational neuroscience work are highlighted through selected studies with neurons and astrocytes by analyzing the existing models qualitatively and assessing the relevance of these models to experimental data. Common strategies to mathematical modeling and computer simulation in neuroscience are summarized for the nontechnical reader. The astrocyte-neuron interactions are then further illustrated by examples of some neurological and neurodegenerative diseases, where the miscommunication between glia and neurons is found to be increasingly important.

Electroencephalographic field influence on calcium momentum waves

Macroscopic electroencephalographic (EEG) fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered is macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered is Ca(2+) waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca(2+) momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π=p+qA (SI units), is calculated, where the charge of Ca(2+) is q=-2e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca(2+) ions, in both classical and quantum mechanics. Molecular scales of Ca(2+) wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca(2+) waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p+qA interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.